Methods of measuring cardiac output using a non-invasively estimated intrapulmonary shunt fraction

ABSTRACT

A method of non-invasively estimating the intrapulmonary shunt in a patient. The method includes non-invasively measuring respiratory flow, respiratory carbon dioxide content, and arterial blood oxygen content. A re-breathing process is employed to facilitate an estimate of the patient&#39;s pulmonary capillary blood flow. Any inaccuracies of the arterial blood oxygen content are corrected to provide a substantially accurate arterial blood oxygen content measurement. The respiratory flow, carbon dioxide content and arterial blood oxygen content measurements, and the pulmonary capillary blood flow estimate are employed to estimate an intrapulmonary shunt of the patient. The invention also includes a method of determining the total cardiac output of the patient which considers the estimated intrapulmonary shunt.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of application Ser. No. 09/150,450,filed Sep. 9, 1998, now U.S. Pat. No. 6,042,550.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of non-invasively measuringthe cardiac output of a patient. Particularly, the present inventionrelates to a method of measuring cardiac output which accounts for theamount of intrapulmonary shunted blood. More particularly, the presentinvention relates to a method of non-invasively estimatingintrapulmonary shunt and considering the intrapulmonary shunt withre-breathing pulmonary capillary blood flow measurements in measuringthe cardiac output.

2. Background of Related Art

Cardiac output is one of various hemodynamic parameters that may bemonitored in critically ill patients. Conventionally, cardiac output hasbeen measured by direct, invasive techniques, such as by thermodilutionusing a Swan-Ganz catheter. Invasive measurement of cardiac output isundesirable because of the potential for harming the patient that istypically associated with the use of such a catheter.

Thus, non-invasive techniques for determining cardiac output have beendeveloped. Cardiac output is the sum of blood flow through the lungsthat participates in gas exchange, which is typically referred to aspulmonary capillary blood flow, and the blood flow that does notparticipate in gas exchange, which is typically referred to asintrapulmonary shunt flow or venous admixture.

The pulmonary capillary blood flow of a patient has been non-invasivelydetermined by employing various respiratory, blood, and blood gasprofile parameters in a derivation of the Fick equation (typicallyeither the O₂ Fick equation or the CO₂ Fick equation), such as by theuse of partial and total re-breathing techniques.

The carbon dioxide Fick equation, which may be employed to determinecardiac output, follows:

 Q_(t)=VCO ₂/(CVCO₂−CaCO₂),

where Q_(t) is the cardiac output of the patient, VCO ₂ is the carbondioxide elimination of the patient, CVCO₂ is the carbon dioxide contentof the venous blood of the patient, and CaCO₂ is the carbon dioxidecontent of the arterial blood of the patient.

The carbon dioxide elimination of the patient may be non-invasivelymeasured as the difference per breath between the volume of carbondioxide inhaled during inspiration and the volume of carbon dioxideexhaled during expiration, and is typically calculated as the integralof the carbon dioxide signal times the rate of flow over an entirebreath. The volume of carbon dioxide inhaled and exhaled may each becorrected for any deadspace or for any intrapulmonary shunt.

The partial pressure of end tidal carbon dioxide (PetCO₂ or etCO₂) isalso measured in re-breathing processes. The partial pressure ofend-tidal carbon dioxide, after correcting for any deadspace, istypically assumed to be approximately equal to the partial pressure ofcarbon dioxide in the alveoli (PACO₂) of the patient or, if there is nointrapulmonary shunt, the partial pressure of carbon dioxide in thearterial blood of the patient (PaCO₂). Conventionally employed Fickmethods of determining cardiac output typically include a direct,invasive determination of CVCO₂ by analyzing a sample of the patient'smixed venous blood. The re-breathing process is typically employed toeither estimate the carbon dioxide content of mixed venous blood (intotal re-breathing) or to obviate the need to know the carbon dioxidecontent of the mixed venous blood (by partial re-breathing) or determinethe partial pressure of carbon dioxide in the patient's venous blood(PVCO₂).

Re-breathing processes typically include the inhalation of a gas mixturewhich includes carbon dioxide. During re-breathing, the carbon dioxideelimination typically decreases. In total re-breathing, carbon dioxideelimination decreases to near zero. In partial re-breathing, carbondioxide elimination does not cease. Thus, in partial re-breathing, thedecrease in carbon dioxide elimination is not as large as that of totalre-breathing.

Re-breathing can be conducted with a re-breathing circuit, which causesa patient to inhale a gas mixture that includes carbon dioxide. FIG. 1schematically illustrates an exemplary re-breathing circuit 50 thatincludes a tubular airway 52 that communicates air flow to and from thelungs of a patient. Tubular airway 52 may be placed in communicationwith the trachea of the patient by known intubation processes, or byconnection to a breathing mask positioned over the nose and/or mouth ofthe patient. A flow meter 72, such as a pneumotachometer, and a carbondioxide sensor 74, which is typically referred to as a capnometer, aredisposed between tubular airway 52 and a length of hose 60, and areexposed to any air that flows through re-breathing circuit 50. Both endsof another length of hose, which is referred to as deadspace 70,communicate with hose 60. The two ends of deadspace 70 are separatedfrom one another by a two-way valve 68, which may be positioned todirect the flow of air through deadspace 70. Deadspace 70 may alsoinclude an expandable section 62. A Y-piece 58, disposed on hose 60opposite flow meter 72 and carbon dioxide sensor 74, facilitates theconnection of an inspiratory hose 54 and an expiratory hose 56 tore-breathing circuit 50 and the flow communication of the inspiratoryhose 54 and expiratory hose 56 with hose 60. During inhalation, gasflows into inspiratory hose 54 from the atmosphere or a ventilator (notshown). During normal breathing, valve 68 is positioned to preventinhaled and exhaled air from flowing through deadspace 70. Duringre-breathing, valve 68 is positioned to direct the flow of exhaled andinhaled gases through deadspace 70.

During total re-breathing, the partial pressure of end-tidal carbondioxide is typically assumed to be equal to the partial pressure ofcarbon dioxide in the venous blood (PVCO₂) of the patient, as well as tothe partial pressure of carbon dioxide in the arterial blood (PaCO₂) ofthe patient and to the partial pressure of carbon dioxide in thealveolar blood (PACO₂) of the patient. The partial pressure of carbondioxide in blood may be converted to the content of carbon dioxide inblood by means of a carbon dioxide dissociation curve.

In partial re-breathing, measurements during normal breathing andsubsequent re-breathing are substituted into the carbon dioxide Fickequation. This results in a system of two equations and two unknowns(carbon dioxide content in the mixed venous blood and cardiac output),from which pulmonary capillary blood flow can be determined withoutknowing the carbon dioxide content of the mixed venous blood.

Known re-breathing techniques for non-invasively determining cardiacoutput are, however, somewhat undesirable since they typically measurepulmonary capillary blood flow and do not account for intrapulmonaryshunt flow.

The failure of conventional non-invasive re-breathing techniques fordetermining cardiac output to account for intrapulmonary shunt wasrecognized, and techniques were developed to estimate the intrapulmonaryshunt. Some intrapulmonary shunt flow (Q_(s)) or shunt fraction(Q_(s)/Q_(t)) or venous admixture estimates employ values obtained frompulse oximetry (SpO₂) and inspiratory oxygen fractions (FiO₂). In B.Österlund et al., A new method of using gas exchange measurements forthe noninvasive determination of cardiac output: clinical experiences inadults following cardiac surgery, Acta Anaesthesiol. Scand. (1995)39:727-732 (“Österlund”), Österlund notes that while pulse oximetrymeasurements provide accurate shunt estimates when FiO₂ is close to 0.21(approximately the fraction of oxygen in the air), when the fraction ofinspired oxygen (FiO₂) exceeds 0.5, as it typically does when a patientis artificially ventilated, the arterial oxygen tension of a patientshould be measured directly (i.e., invasively). Moreover, as FIG. 2illustrates, as the blood becomes about 95-100% saturated with oxygen,due to the steepness of the oxygen tension-saturation curve of FIG. 2,precise and accurate arterial blood oxygen saturation measurements(SaO₂) are necessary to accurately determine the partial pressure ofoxygen in a patient's arterial blood. Thus, since pulmonary capillaryblood flow measurements are often taken while a patient's breathing isartificially ventilated, and since FiO₂ is typically greater than about0.5, the technique disclosed in Österlund often undesirably requiresinvasive measurement of SaO₂.

Accordingly, there is a need for a method of non-invasively andaccurately estimating intrapulmonary shunt, as well as a method ofaccounting for the estimated intrapulmonary shunt in determining thecardiac output of a patient by re-breathing techniques.

SUMMARY OF THE INVENTION

The methods of the present invention address each of the foregoingneeds.

The present invention includes a method of non-invasively estimating theintrapulmonary shunt, pulmonary capillary blood flow and cardiac outputof a patient. The shunt-estimating method according to the presentinvention includes non-invasively measuring the pulmonary capillaryblood flow of the patient, measuring a volume of carbon dioxide exhaledby the patient, determining the difference between the end capillaryoxygen content and the arterial oxygen content of the patient's blood,dividing the difference by the volume of carbon dioxide exhaled by thepatient, and multiplying the difference by the patient's pulmonarycapillary blood flow and by the patient's respiratory quotient (RQ). Therespiratory quotient is the volume of carbon dioxide exhaled by thepatient divided by the volume of oxygen exhaled by the patient. Therespiratory quotient may be an assumed value (e.g., RQ=0.86).

The pulmonary capillary blood flow of the patient may be determined byknown techniques, such as partial or total re-breathing techniques.

The patient's cardiac output (Q_(t)) includes a portion, which istypically identified as pulmonary capillary blood flow Q_(pcbf), thatflows through pulmonary capillaries 164 (FIG. 5) and participates in gasexchange in the lungs 150, and a portion that does not participate inblood gas exchange, which is referred to as the intrapulmonary shunt165, venous admixture, shunted blood, or simply as “shunt”. Thecorrected cardiac output may be determined by adding the non-invasivelymeasured volume rate of pulmonary capillary blood flow (Q_(pCbf)) andthe volume rate of flow of the intrapulmonary shunt flow of the patient(Q_(s)) by the following equation:

Q_(t)=Q_(pcbf)+Q_(s).

Alternatively, a patient's corrected cardiac output may be determined asfollows:

Q_(t)=Q_(pcbf)/(1−Q_(s)/Q_(t)),

where Q_(s)/Q_(t) is the intrapulmonary shunt fraction.

The uncorrected volume/rate of the patient's pulmonary capillary bloodflow (Q_(pcbf)) is preferably measured by non-invasive techniques, suchas known partial or total re-breathing techniques, and may be employedwith a variety of carbon dioxide, respiratory flow and pulse oximetryapparatus.

The shunt fraction of the patient's pulmonary capillary blood flow maybe derived from various respiratory profile parameters, many of whichmay also be measured by non-invasive techniques. Q_(s)/Q_(t) may beestimated in accordance with the following equation:${{Q_{s}/Q_{t}} = \frac{{{Cc}^{\prime}O_{2}} - {CaO}_{2}}{{{Cc}^{\prime}O_{2}} - {{Cv}O}_{2}}},$

where Cc′O₂ is the end-capillary oxygen content, CaO₂ is the arterialoxygen content, and CVO₂ is the mixed venous oxygen content. Thedenominator of the preceding formula (Cc′O₂−CVO₂) can be derived fromthe Fick oxygen equation that is typically employed in knownre-breathing techniques for determining pulmonary capillary blood flow:

Cc′O₂−CVO₂=VO ₂/Q_(pcbf)

Since the respiratory quotient is the ratio of the carbon dioxideelimination (VCO ₂) to the amount of oxygen consumed (VO ₂) by thepatient, as defined by the following equation:

RQ=VCO ₂/VO ₂,

VCO ₂/RQ may be substituted for VO ₂. Such substitution of VCO ₂/RQ forVO ₂ is preferred because it is difficult to accurately measure VO ₂,especially in patients who require an elevated fraction of inspiredoxygen. Moreover, RQ can be assumed with accuracy (typically about 0.7to 1.0, and more particularly about 0.8 to 0.9 or 0.86). Thus,

Cc′O₂−CVO₂=VCO ₂/(Q_(pcbf)·RQ).

Accordingly, the shunt fraction, Q_(s)/Q_(t), may be estimated by thefollowing formula:${Q_{s}/Q_{t}} = {\frac{\frac{{{Cc}^{\prime}O_{2}} - {CaO}_{2}}{V_{{CO}_{2}}}}{Q_{pcbf} \cdot {RQ}}.}$

The VCO ₂ measurement is preferably based on the alveolar CO₂ output ofthe patient, and may be measured by known re-breathing techniques.

The end-capillary oxygen content, Cc′O₂, may be calculated by thefollowing equation:

Cc′O₂=(P_(A)O₂·α)+(Sc′O₂·Hb_(capacity)·Hb_(conc)),

where the alveolar oxygen tension of the patient may be calculated bythe following formula:

PAO₂−(FiO₂·(P_(bar)−P_(H) ₂ _(O)))−(PaCO₂/RQ·(1−(FiO₂·(1−RQ)))),

where p_(bar) is the barometric pressure, P_(H) ₂ _(O) is the saturatedwater vapor pressure of a sample at ambient temperature and PaCO₂ is thepartial pressure of CO₂ in the patient's arterial blood, which may beassumed, calculated as known in the art from non-invasively obtainedarterial blood gas data, or obtained by direct measurement. The bloodoxygen solubility coefficient (α), the end-capillary blood saturation(Sc′O₂), hemoglobin concentration (Hb_(conc)), and hemoglobin capacity(Hb_(capacity)) values may each be assumed values or determined by knowntechniques.

The arterial oxygen content, CaO₂, may be calculated by the followingequation:

CaO₂=(PaO₂·α)+(SaO₂·Hb_(capacity)·Hb_(conc)).

Since PaO₂ is a function of SaO₂, which may be approximated by SpO₂, thepartial pressure of the patient's arterial oxygen, PaO₂, may becalculated from the oxygen saturation (SaO₂) of the patient's arterialblood using an invertible version of the blood oxygen tension-saturationrelationship, as represented by the Lobdell equation. Lobdell, D. D., Aninvertible simple equation for computation of blood O₂ dissociationrelations, J Appl. Physiol. (1981) 971-973.

Arterial blood oxygen saturation, SaO₂, may be determined by known pulseoximetry (SpO₂) techniques. Pulse oximetry techniques may providesomewhat inaccurate blood oxygen saturation data (i.e., SaO₂ values). Asthe inverted tension-saturation curve is relatively steep at about95-100% blood oxygen saturation, it is, therefore, difficult toaccurately derive PaO₂ from SaO₂. Thus, the SpO₂ measurement iscorrected to provide a more accurate PaO₂ value.

Alternatively, the measured SaO₂ or PaO₂ and FiO₂ of the patient may beemployed with an iso-shunt diagram or one or more equations that may beemployed to generate an iso-shunt diagram to non-invasively estimate theintrapulmonary shunt fraction of the cardiac output of a patient.

Once a non-invasive determination of a patient's pulmonary capillaryblood flow has been made and the intrapulmonary shunt flow or shuntfraction of the patient estimated, the patient's cardiac output (Q_(t))may be determined.

The advantages of the present invention will become apparent to those ofskill in the art through a consideration of the ensuing description, theaccompanying drawings, and the appended claims.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a schematic representation of an exemplary re-breathingcircuit that may be employed with the methods of the present invention;

FIG. 2 is a line graph of an inverse Lobdell relation, which illustratesthe relatively large difference in PaO₂ values derived from relativelyclose SpO₂ values—in the 95-100% range—and, thus, the potential forerror when inaccurate SpO₂ measurements are made;

FIG. 3 is a schematic representation which illustrates the variouscomponentry that may be utilized to measure respiratory profileparameters that are employed in the methods of the present invention;

FIG. 4 is a schematic representation which illustrates a pulse oximetrysensor and associated monitor, which may be employed in association withthe methods of the present invention;

FIG. 5 is a schematic representation of the lungs of a patient;

FIG. 6 is a flow diagram of a preferred embodiment of the method of thepresent invention;

FIG. 7 is an iso-shunt diagram that is useful in determining theintrapulmonary shunt fractions of the cardiac output of a patient inaccordance with another embodiment of the methods; and

FIG. 8 is another iso-shunt diagram that may be employed to determinethe intrapulmonary shunt fraction of the cardiac output of a patient.

DETAILED DESCRIPTION OF THE INVENTION

The present invention includes a method of estimating the flow, orfraction, of blood that does not participate in the exchange of oxygen(O₂) and carbon dioxide (CO₂) in the pulmonary capillaries, which isreferred to as “intrapulmonary shunt”, “venous admixture”, “shuntedblood”, or simply as “shunt”. The present invention also includes amethod of calculating cardiac output based on the shunt estimate.

Due to the difficulty of measuring the amount of oxygen consumed by apatient (VO ₂), especially in patients who require an elevated fractionof inspired oxygen, pulmonary capillary blood flow (Q_(pcbf)), cardiacoutput (CO), and the estimated shunt fraction are preferably measured interms of the amount of carbon dioxide excreted into the lungs of thepatient, which is typically measured in terms of carbon dioxideelimination (VCO ₂). The Fick equation for measurement of cardiacoutput, in terms of CO₂, is:

Q_(t)=VCO ₂/(CVCO₂−CaCO₂).

Measuring Respiratory, Blood and Blood Gas Profile Parameters

With reference to FIG. 6, calculating pulmonary capillary blood flow inaccordance with the method of the present invention includes measuringthe flow rates and CO₂ fraction of gas mixtures that are inhaled andexhaled by a patient 10 over the course of the patient's breathing, at110. With reference to FIG. 3, a flow sensor 12 of a known type, such asthe differential-pressure type respiratory flow sensors manufactured byNovametrix Medical Systems Inc. (“Novametrix”) of Wallingford, Conn.(e.g, the Pediatric/Adult Flow Sensor (Catalog No. 6717) or the NeonatalFlow Sensor (Catalog No. 6718)), which may be operatively attached to aventilation apparatus (not shown), as well as respiratory flow sensorsbased on other operating principles and manufactured and marketed byothers, may be employed to measure the flow rates of the breathing ofpatient 10. A CO₂ sensor 14, such as the CAPNOSTAT® CO₂ sensor and acomplementary airway adapter (e.g., the Pediatric/Adult Single PatientUse Airway Adapter (Catalog No. 6063), the Pediatric/Adult ReusableAirway Adapter (Catalog No. 7007), or the Neonatal/Pediatric ReusableAirway Adapter (Catalog No. 7053)), which are manufactured byNovametrix, as well as mainstream or sidestream CO₂ sensors manufacturedor marketed by others, may be employed to measure the CO₂ fraction ofgas mixtures that is inhaled and exhaled by patient 10. Flow sensor 12and CO₂ sensor 14 are connected to a flow monitor 16 and a CO₂ monitor18, respectively, each of which may be operatively associated with acomputer 20 so that data from the flow and CO₂ monitors 16 and 18representative of the signals from each of flow sensor 12 and CO₂ sensor14 may be detected by the computer 20 and processed according toprogramming (e.g., by software) thereof Preferably, raw flow and CO₂signals from the flow monitor and CO₂ sensor are filtered, as known inthe art, to remove any significant artifacts. As respiratory flow andCO₂ pressure measurements are made, the respiratory flow and CO₂pressure data may be stored by computer 20. Thus, pulmonary capillaryblood flow may be calculated, in accordance with the foregoing equationor by any other equation known in the art, by computer 20.

Each breath, or breathing cycle, of patient 10 may be delineated asknown in the art, such as by continually monitoring the flow rate of thebreathing of patient 10.

Referring now to FIG. 4, at 120 of the flow diagram of FIG. 6, bloodoxygen measurements may be made, at 122 of FIG. 6, by non-invasivemeans, such as by a pulse oximetry sensor 30 of a type known in the art,such as the OXYSNAP™ or Y-SENSOR™, both of which are manufactured byNovametrix. Pulse oximetry sensor 30 includes a light emitting diode(LED) assembly 32 and a photodiode 34 which are positionable on oppositesides of an appendage of the body of a patient, such as a finger 11,hand, toe, heel, foot, ear lobe, nose, or tongue. SpO₂ signals, whichmay be conveyed from pulse oximetry sensor 30 to computer 20, as knownin the art, such as by a cable connector 36, are subsequently employedin the methods of the present invention.

Various other values that are employed in the methods of the presentinvention may be measured separately or assumed, then used in themethods, such as by entering these values into computer 20.

Preliminarily Determining Pulmonary Capillary Blood Flow

Referring again to the flow diagram of FIG. 6, at 112, for eachbreathing cycle, the partial pressure of end-tidal CO₂, carbon dioxideelimination (VCO ₂), the fraction of inspired, or “mixed inspired”, CO₂and the airway deadspace are calculated. End-tidal CO₂ is measured asknown in the art. Carbon dioxide elimination is typically calculated asthe integral of the respiratory flow over a breathing cycle (inmilliliters) multiplied by fraction of CO₂ over the entire breath. Thefraction of inspired CO₂ is the integral of CO₂ fraction times the airflow during inspiration, divided by the volume (in milliliters) ofinspired gas.

The values of VCO ₂ and PetCO₂ may be filtered by employing athree-point median filter, which uses a median value from the mostrecent value of recorded VCO ₂ and PetCO₂ values and the two values thatprecede the most recent measured value, as known in the art.

Preferably, when calculating VCO ₂, the VCO ₂ value is corrected toaccount for anatomic deadspace and alveolar deadspace. With reference toFIG. 5, the lungs 150 of a patient may be described as including atrachea 152, two bronchi 154 and numerous alveoli 160, 162. Theanatomic, or “serial”, deadspace of lungs 150 includes the volume of thetrachea 152, bronchi 154, and other components of lungs 150 which holdgases, but do not participate in gas exchange. The anatomic deadspaceexists approximately in the region located between arrows A and B. Theso-called “shunted” blood bypasses pulmonary capillaries by way of anintrapulmonary shunt 165.

Lungs 150 typically include alveoli 160 that are in contact with bloodflow and which can facilitate oxygenation of the blood, which arereferred to as “perfused” alveoli, as well as unperfised alveoli 162.Both perfused alveoli 160 and unperfused alveoli 162 may be ventilated.The volume of unperfused alveoli is the alveolar deadspace.

Perfused alveoli 160 are surrounded by and in contact with pulmonarycapillaries 164. As deoxygenated blood 166 enters pulmonary capillaries164, oxygen binds to the hemoglobin molecules of the red blood cells ofthe blood and CO₂ is released from the hemoglobin. Blood that exitspulmonary capillaries 164 in the direction of arrow 170 is referred toas oxygenated blood 168. In alveoli 160 and 162, a volume of gas knownas the functional residual capacity (FRC) 171 remains followingexhalation. The alveolar CO₂ is expired from a portion 172 of each ofthe alveoli 160 that is evacuated, or ventilated, during exhalation.

The ventilated portion 178 of each of the unperfused alveoli 162 mayalso include CO₂. The CO₂ of ventilated portion 178 of each of theunperfused alveoli 162, however, is not the result of O₂ and CO₂exchange in that alveolus. Since the ventilated portion 178 of each ofthe unperfused alveoli 162 is ventilated in parallel with the perfusedalveoli, ventilated portion 178 is typically referred to as “parallel”deadspace (PDS). Unperfused alveoli 162 also include a FRC 176, whichincludes a volume of gas that is not evacuated during a breath.

In calculating the partial pressure of CO₂ in the alveoli (PACO₂) of thepatient, the FRC and the partial pressure of CO₂ in the paralleldeadspace in each of the unperfused alveoli 162 is preferably accountedfor. FRC may be estimated as a function of body weight and the airwaydeadspace volume by the following equation:

FRC=FRC-factor·(airway deadspace+offset value),

where FRC-factor is either an experimentally determined value or isbased on published data (e.g., “experiential” data) known in the art,and the offset value is a fixed constant which compensates for breathingmasks or other equipment components that may add deadspace to thebreathing circuit and thereby unacceptably skew the relationship betweenFRC and deadspace.

The partial pressure of CO₂ in the parallel deadspace (CO_(2PDS)) may becalculated from the mixed inspired CO₂ (Vi_(CO2)) added to the productof the serial deadspace multiplied by the end tidal CO₂ of the previousbreath (PetCO₂(n−1)). Because the average partial pressure of CO₂ in theparallel deadspace is equal to the partial pressure of CO₂ in theparallel deadspace divided by the tidal volume (V_(t)) (i.e., the totalvolume of one respiratory cycle, or breath), the partial pressure of CO₂in the parallel deadspace may be calculated on a breath-by-breath basis,as follows:

PCO_(2 PDS)(n)=[FRC/(FRC+V_(t))]·PCO_(2 PDS)(n−1)+(P_(bar)·(([Vi_(CO2)+deadspace·(PetCO₂(n−1)/P_(bar))]/V_(t))·[V_(t)/(V_(t)+FRC)])),

where (n) indicates a respiratory profile parameter (in this case, thepartial pressure of CO₂ in the parallel deadspace) from the most recentbreath and (n−1) indicates a respiratory profile parameter from theprevious breath.

The partial pressure of end-tidal CO₂, which is assumed to besubstantially equal to a weighted average of the partial pressure of CO₂in all of the perfused and unperfused alveoli of a patient, may then becalculated as follows:

PetCO₂=®·PACO₂)+(1−r)PCO_(2 PDS),

where r is the perfusion ratio, which is calculated as the ratio ofperfused alveolar ventilation to the total alveolar ventilation, or(V_(A)−V_(PDS))/V_(A). The perfusion ratio may be assumed to be about0.95 or estimated as known in the art.

By rearranging the previous equation, the alveolar CO₂ partial pressureof the patient may be calculated. Preferably, alveolar CO₂ partialpressure is calculated from the end-tidal CO₂ and the CO₂ in theparallel deadspace, as follows:

PACO₂=[PetCO₂−(1−r)PCO_(2PDS)]/r.

The alveolar CO₂ partial pressure may then be converted to alveolarblood CO₂ content (CACO₂) using an equation, such as the following:

CACO₂=(6.957·Hb_(conc)+94.864)·1n(1+0.1933(PACO₂)),

where CACO₂ is the content of CO₂ in the alveolar blood and Hb is theconcentration of hemoglobin in the blood of the pulmonary capillaries.J. M. Capek and R. J. Roy, IEEE Transactions on Biomedical Engineering(1988) 35(9):653-661. In some instances, a hemoglobin count and,therefore, the hemoglobin concentration are available and may beemployed in calculating the CO₂ content. If a hemoglobin count orconcentration is not available, another value that is based uponexperiential or otherwise known data (e.g., 11.0 g/dl) may be employedin calculating the alveolar CO₂ content.

In calculating VCO ₂, the FRC and alveolar deadspace of the lungs of apatient may be accounted for by multiplying the FRC by the change in endtidal partial pressure, such as by the following equation:

VCO _(2 corrected)=VCO ₂+FRC×ΔPetCO₂/P_(bar),

where ΔPetCO₂ is the breath-to-breath change in PetCO₂.

Baseline PetCO₂ and VCO ₂ values, which are also referred to as “beforere-breathing PetCO₂” and “before re-breathing VCO ₂”, respectively,occur during normal breathing and may be calculated as the average of agroup of samples taken before the re-breathing process (e.g., theaverage of all samples between about 27 and 0 seconds before the startof a known re-breathing process). A VCO ₂ value, which is typicallyreferred to as “during re-breathing VCO ₂”, is calculated during there-breathing process. “During re-breathing VCO ₂” may be calculated asthe average VCO ₂ during the interval of 25 to 30 seconds into there-breathing period.

The content of CO₂ in the alveolar blood during the re-breathing processmay then be calculated by employing a regression line, which facilitatesprediction of the stable, or unchanging, content of alveolar CO₂.Preferably, PACO₂ is plotted against the breath-to-breath change incontent of alveolar CO₂ (ΔPACO₂). A graph line that is defined by theplotted points is regressed, and the intersection between PACO₂ and zeroΔPACO₂ is the predicted stable content of alveolar CO₂.

Pulmonary capillary blood flow may then be calculated as follows:$Q_{pcbf} = {\frac{\left\lbrack {{{before}\quad {re}\text{-}{breathing}\quad V_{{CO}_{2}}} - {{during}\quad {re}\text{-}{breathing}\quad V_{{CO}_{2}}}} \right\rbrack}{\left\lbrack {{{during}\quad {re}\text{-}{breathing}\quad C_{A}{CO}_{2}} - {{before}\quad {re}\text{-}{breathing}\quad C_{A}{CO}_{2}}} \right\rbrack}.}$

Alternative differential Fick methods of measuring pulmonary capillaryblood flow or cardiac output may be employed in place of the embodimentof the re-breathing method disclosed herein. Such alternativedifferential Fick methods typically require a brief change of PetCO₂ andVCO ₂ in response to a change in effective ventilation. This briefchange can be accomplished by adjusting the respiratory rate,inspiratory and/or expiratory times, or tidal volume. A brief change ineffective ventilation may also be effected by adding CO₂, eitherdirectly or by re-breathing. An exemplary differential Fick method thatmay be employed with the present invention, which is disclosed inGedeon, A. et al. in 18 Med. & Biol. Eng. & Comput. 411-418 (1980),employs a period of increased ventilation followed immediately by aperiod of decreased ventilation.

Estimating Shunt Fraction

After a Q_(pcbf) has been determined by non-invasive means, theintrapulmonary shunt fraction of the cardiac output of the patient maybe estimated. The method of estimating intrapulmonary shunt according tothe present invention also includes non-invasively determining thedifference between the end capillary oxygen content and the arterialoxygen content of the patient's blood, dividing the difference by thevolume of carbon dioxide exhaled by the patient, and multiplying thedifference by the patient's pulmonary capillary blood flow (Q_(pcbf))and by the patient's respiratory quotient (RQ).

The shunt fraction of the patient's cardiac output may be derived fromvarious respiratory profile parameters, many of which may also bemeasured by non-invasive techniques. Q_(s)/Q_(t) may be estimated inaccordance with the following equation:${{Q_{s}/Q_{t}} = \frac{{{Cc}^{\prime}O_{2}} - {CaO}_{2}}{{{Cc}^{\prime}O_{2}} - {{Cv}O}_{2}}},$

where Cc′O₂ is the end-capillary oxygen content, CaO₂ is the arterialoxygen content, and CVO₂ is the mixed venous oxygen content. Thedenominator of the preceding formula (Cc′O₂−CVO₂) can be derived fromthe Fick oxygen equation that has been conventionally employed inre-breathing techniques for determining cardiac output:$Q_{pcbf} = {\frac{{VO}_{2}}{{{Cc}^{\prime}O_{2}} - {{Cv}O}_{2}}.}$

This equation may be rewritten as:

Cc′O₂−CVO₂=VO ₂/Q_(pcbf)

Moreover, since the respiratory quotient (RQ) is the ratio of the carbondioxide elimination (VCO ₂) to the oxygen uptake (VO ₂) of a patient, asdefined by the following equation:

RQ=VCO ₂/VO ₂,

and because of the difficulty of accurately measuring VO ₂, especiallyin patients who require an elevated fraction of inspired oxygen, and theaccuracy with which RQ can be assumed (typically about 0.7 to 1.0, andmore particularly about 0.8 to 0.9 or 0.86), VCO ₂/RQ may be substitutedfor VO ₂. Thus,

Cc′O₂−CVO₂=VCO ₂/(Q_(pcbf)·RQ).

Accordingly, the shunt fraction, Q_(s)/Q_(t), may be estimated, at 130of FIG. 6, by the following formula:${Q_{s}/Q_{t}} = {\frac{\frac{{{Cc}^{\prime}O_{2}} - {CaO}_{2}}{V_{{CO}_{2}}}}{Q_{pcbf} \cdot {RQ}}.}$

VCO ₂, which was determined above in the calculation of the pulmonarycapillary blood flow of the patient, is the CO₂ elimination of thepatient.

Alternatively, VO₂ may be measured as known in the art, and RQ can becalculated rather than assumed. As another alternative, the VO₂measurement may be divided by Q_(pcbf) to directly determine Cc′O₂−CVO₂,in which case the following formula may be employed to estimate theshunt fraction:${Q_{s}/Q_{t}} = \frac{\frac{{{Cc}^{\prime}O_{2}} - {CaO}_{2}}{{VO}_{2}}}{Q_{pcbf}}$

The end-capillary oxygen content, Cc′O₂, may be calculated, at 114 ofFIG. 6, by the following equation:

Cc′O₂=(P_(A)O₂·α)+(Sc′O₂·Hb_(capacity)·Hb_(conc)),

where the blood oxygen solubility coefficient (α), end capillary bloodsaturation (Sc′O₂), hemoglobin concentration (Hb_(conc)), and hemoglobincapacity (Hb_(capacity)) values may each be assumed, or determined byknown techniques, such as by direct chemical analysis of the blood.

The alveolar oxygen tension of the patient may be calculated by thefollowing formula:

PAO₂=(FiO₂·(P_(bar)−P_(H) ₂ _(O)))−(PaCO₂/RQ·(1−(FiO₂·(1−RQ)))),

where P_(bar) is barometric pressure, P_(H) ₂ _(O) is the saturatedwater vapor pressure of a sample at ambient temperature, and PaCO₂ isthe partial pressure of CO₂ in the patient's arterial blood, which maybe assumed, calculated as known in the art from non-invasively obtainedarterial blood gas data, or obtained by direct measurement.

The oxygen content of the patient's arterial blood, CaO₂, may becalculated, at 126 of FIG. 6, by the following equation:

CaO₂=(PaO₂·α)+(SaO₂·Hb_(capacity)·Hb_(conc)).

Since PaO₂ is a function of SaO₂, which may be non-invasively estimatedby measuring SpO₂ (see FIG. 6, at 124), the partial pressure of O₂ inthe patient's arterial blood, PaO₂, may be calculated from the oxygensaturation (SaO₂) of the patient's arterial blood by employing aninvertable version of a blood oxygen tension-saturation curve. Arterialblood oxygen saturation is determined non-invasively by knowntechniques, such as by pulse oximetry (SpO₂), as discussed previously inreference to FIG. 4.

Due to the inaccuracy of pulse oximetry measurements, which aretypically in the range of about 2-3% and fairly consistent for aspecific pulse oximeter, as well as the steepness of thetension-saturation curve between blood oxygen saturations of about95-100%, a correction summand, which is also referred to as a correctionfactor, is employed in determining the oxygen saturation and partialpressure of oxygen in the arterial blood.

The correction summand may be an assumed value (e.g., 2 or 3%) based onexperiential error of a known degree when a specific type of pulseoximeter or a particular model of pulse oximeter of a particularmanufacturer is employed to measure SpO₂. Alternatively, the correctionsummand may be determined by comparing a direct SaO₂ measurement fromblood gas chemical analysis with an SpO₂ measurement taken by a pulseoximeter.

The correction summand may then be employed in combination withsubsequent pulse oximetry measurements to modify these pulse oximetrymeasurements and more accurately determine the partial pressure ofoxygen in the patient's arterial blood. This may be done by adding acorrection summand to the SpO₂ measurement or subtracting a correctionsummand from the SpO₂ measurement, by generating an equation to convertthe SpO₂ measurement to a more accurate value, or by generating aspecial function in which the non-invasively measured, possibly somewhatinaccurate, SpO₂ measurement is employed to accurately determine SaO₂ orPaO₂. The SaO₂ or PaO₂ value may then be employed in the precedingequation to facilitate an accurate, non-invasive determination of thepatient's intrapulmonary shunt.

In another embodiment of the method of estimating intrapulmonary shunt,the SaO₂ or PaO₂ of a patient may be non-invasively determined andcorrected as described above. The patient's FiO₂ is also determined, asknown in the art, such as by a respiratory measurement or from a setfraction, or value, of oxygen in a gas mixture with which the patient isartificially ventilated. An iso-shunt diagram, which is also referred toas an iso-shunt plot, such as that disclosed in S. R. Benatar et al.,The use of iso-shunt lines for control of oxygen therapy, Brit. JAnaesth. (1973) 45:711, and in NUNN, J. F., NUNN'S APPLIED RESPIRATORYPHYSIOLOGY 184, FIG. 8.10 (4th ed.) and shown in FIG. 7, may then beemployed with the SaO₂ or PaO₂ and FiO₂ measurements to determine theintrapulmonary shunt fraction of the cardiac output of the patient.

The intrapulmonary shunt fraction may be similarly estimated byincorporating the measured SaO₂ or PaO₂ and FiO₂ values into thefollowing series of equations that Nunn used to generate the iso-shuntdiagram of FIG. 7 from FiO₂ and PaO₂ measurements:

 PAO₂=((P_(bar)−P_(H) ₂ _(O))·FiO₂)−(PaCO₂/RQ)(1−FiO₂·(1−RQ)),

where PaO₂ is the partial pressure of oxygen in the alveoli of thepatient; P_(bar), the barometric pressure, is assumed to be 101.33 kPa;P_(H) ₂ _(O), or water pressure, is assumed to be 6.27 kPa; PaCO₂, thepartial pressure of carbon dioxide in the arterial blood of the patient,or the arterial carbon dioxide tension, is assumed to be 5.33 kPa; andRQ is assumed to be 0.8 (alternatively, each of these parameters may beassumed to be equal to a different value or measured by techniques knownin the art);

ScO₂=(PAO₂ ³+2.667·PAO₂)/(PAO₂ ³+2.667·PAO₂+55.47),

or the Severinghaus equation for conversion from partial pressure ofoxygen to oxygen saturation, where ScO₂ is the oxygen saturation of theend capillary blood of the patient; other equations for convertingpartial pressure of oxygen to oxygen saturation, such as the Lobdellequation, may also be employed;

Cc′O₂=(PAO₂·α)+(ScO₂·Hb_(cap)·Hb_(conc)),

where Hb_(cap) is assumed to be 1.31 (ml/g) and Hb_(conc) is assumed tobe 14 g/dl;

SaO₂=(1·PaO₂ ³+2.667·PaO₂)/(1·PaO₂ ³+2.667·PaO₂+55.47),

or the Severinghaus equation for conversion from partial pressure ofoxygen to oxygen saturation, where SaO₂ is the oxygen saturation of thearterial blood of the patient and PaO₂ is the partial pressure of oxygenin the arterial blood of the patient; other equations for convertingpartial pressure of oxygen to oxygen saturation, such as the Lobdellequation, may also be employed;

CaO₂=(PaO₂·α)+(SaO₂·Hb_(cap)·Hb_(conc)),

where Hb_(cap) is assumed to be 1.31 (mlg) and Hb_(conc) is assumed tobe 14 g/dl; and

Q_(s)/Q_(t)=100·(Cc′O₂−CaO₂)/((CaO₂−CVO₂)+(Cc′O₂−CaO₂)),

where (CaO₂−CVO₂), the arterial-venous oxygen gradient of the patient,is assumed to remain substantially constant over short periods of time(e.g., one, five, or ten minutes).

Other iso-shunt equations or diagrams are also useful with the correctedSaO₂ and PaO₂ values of the present invention to estimate theintrapulmonary shunt of a patient, such as the equation and graphsdisclosed in Dean, J. M., Wetzel, R. C., and Rogers, M. C., Arterialblood gas derived variables as estimates of intrapulmonary shunt incritically ill children, Crit. Care Med. 13(12):1029-1033(1985)(“Dean”). The equation of Dean:${{Q_{s}/Q_{t}} = \frac{({Hgb})(1.34)\left( {1 - {SaO}_{2}} \right)}{\left. \left( {{({Hgb})(1.34)\left( {1 - {SaO}_{2}} \right)} + {CaO}_{2} - {CvO}_{2}} \right) \right)}},$

where Hgb is the hemoglobin concentration of the patient, may beemployed to estimate the intrapulmonary shunt fraction of the cardiacoutput of the patient. Alternatively, SaO₂ may be employed with thegraph of FIG. 8, which is depicted in Dean, to estimate theintrapulmonary shunt fraction.

Other exemplary equations and diagrams that may be employed with theSaO₂ or PaO₂ values determined in accordance with the present inventionto estimate the intrapulmonary shunt fraction of the cardiac output of apatient are disclosed in Hope, D. A. et al., Non-invasive estimation ofvenous admixture: validation of a new formula, Brit. J Anaesth. (1995)74:538-543 and Sapsford, D. J. and Jones, J. G., The PiO₂ vs. SpO₂diagram: a non-invasive measure of pulmonary oxygen exchange, Eur. J.Anaesth. (1995) 12:375-386.

When a non-invasive pulmonary capillary blood flow (Q_(pcbf)) has beendetermined and the shunt fraction (Q_(s)/Q_(t)) estimated, the patient'scardiac output (Q_(t)) may be determined.

Calculating Cardiac Output

The patient's cardiac output may be determined by adding thenon-invasively measured volumetric rate of pulmonary capillary bloodflow (Q_(pcbf)) and the volumetric rate of flow of the patient's shuntedblood (Q_(s)) by the following equation:

Q_(t)=Q_(pcbf)+Q_(s).

Alternatively, the preceding equation may be re-written so that apatient's total cardiac output may also be determined from the shuntfraction (Q_(s)/Q_(t)) and pulmonary capillary blood flow as follows:

Q_(t)=Q_(pcbf)/(1−Q_(s)/Q_(t)).

Although the foregoing description contains many specifics, these shouldnot be construed as limiting the scope of the present invention, butmerely as providing illustrations of some of the presently preferredembodiments. Similarly, other embodiments of the invention may bedevised which do not depart from the spirit or scope of the presentinvention. Features from different embodiments may be employed incombination. The scope of the invention is, therefore, indicated andlimited only by the appended claims and their legal equivalents, ratherthan by the foregoing description. All additions, deletions andmodifications to the invention as disclosed herein which fall within themeaning and scope of the claims are to be embraced thereby.

What is claimed is:
 1. A method of estimating an intrapulmonary shunt ofa patient, comprising: determining a respiratory flow and a respiratorycarbon dioxide fraction of respiration of the patient; calculating acarbon dioxide elimination of the patient; calculating an end capillaryblood oxygen content of the patient; determining an arterial bloodoxygen saturation of the patient; and calculating an intrapulmonaryshunt fraction with said end capillary blood oxygen content, saidarterial blood oxygen saturation, and said carbon dioxide elimination.2. The method of claim 1, wherein said calculating said intrapulmonaryshunt fraction also includes employing a respiratory quotient of thepatient.
 3. The method of claim 2, further comprising measuring saidrespiratory quotient.
 4. The method of claim 2, further comprisingestimating said respiratory quotient.
 5. The method of claim 2, furthercomprising assuming said respiratory quotient.
 6. The method of claim 1,wherein said determining said arterial blood oxygen saturation iseffected by a technique comprising pulse oximetry.
 7. The method ofclaim 1, further comprising correcting for an inaccuracy of saidarterial blood oxygen saturation.
 8. The method of claim 7, wherein saidcorrecting for said inaccuracy comprises modifying said arterial bloodoxygen saturation by a correction summand.
 9. The method of claim 8,wherein said correction summand comprises an assumed value.
 10. Themethod of claim 9, wherein said assumed value comprises about 2% to 3%of said arterial blood oxygen saturation.
 11. The method of claim 8,further comprising determining said correction summand.
 12. The methodof claim 11, wherein said determining said correction summand comprisesdirectly obtaining another arterial blood oxygen saturation measurementand comparing said another arterial blood oxygen saturation measurementto said arterial blood oxygen saturation.
 13. The method of claim 7,wherein said correcting for said inaccuracy comprises generating anequation for converting said arterial blood oxygen saturation to asubstantially accurate value.
 14. The method of claim 13, furthercomprising directly obtaining another arterial blood oxygen saturationmeasurement and comparing said another arterial blood oxygen saturationmeasurement to said arterial blood oxygen saturation.
 15. The method ofclaim 1, further comprising employing said arterial blood oxygensaturation to determine an arterial blood oxygen content of the patient.16. The method of claim 1, further comprising determining an alveolarpartial pressure of oxygen of the patient.
 17. The method of claim 7,wherein said correcting for said inaccuracy comprises modifying alveolarpartial pressure of oxygen.
 18. The method of claim 1, wherein saidcalculating said end capillary blood oxygen content comprisesdetermining an end tidal partial pressure of oxygen.
 19. The method ofclaim 1, wherein said calculating said end capillary blood oxygencontent comprises determining an end tidal partial pressure of carbondioxide.
 20. The method of claim 1, further comprising estimating apulmonary capillary blood flow of the patient.
 21. The method of claim20, wherein said estimating said pulmonary capillary blood flowcomprises re-breathing.
 22. The method of claim 21, wherein saidre-breathing comprises partial or total re-breathing.
 23. The method ofclaim 20, wherein said estimating said pulmonary capillary blood flowcomprises adjusting a respiratory rate.
 24. The method of claim 20,wherein said estimating said pulmonary capillary blood flow comprisesadjusting a period of inspiration or expiration.
 25. The method of claim20, wherein said estimating said pulmonary capillary blood flowcomprises adjusting a tidal volume.
 26. The method of claim 20, whereinsaid estimating said pulmonary capillary blood flow comprises adding avolume of carbon dioxide to ventilation of the patient.
 27. The methodof claim 20, wherein said pulmonary capillary blood flow is employed todetermine an intrapulmonary shunt flow of the patient.
 28. The method ofclaim 20, wherein said pulmonary capillary blood flow is employed todetermine a cardiac output of the patient.
 29. A method of determiningan intrapulmonary shunt fraction of a patient, comprising:non-invasively determining an oxygen saturation of arterial blood of thepatient; determining a fraction of inspired oxygen of the patient;determining a pulmonary capillary blood flow of the patient; andemploying said oxygen saturation of arterial blood and said fraction ofinspired oxygen to determine the intrapulmonary shunt fraction.
 30. Themethod of claim 29, wherein said determining said pulmonary capillaryblood flow comprises re-breathing.
 31. The method of claim 29, whereinsaid employing comprises employing said oxygen saturation of arterialblood and said fraction of inspired oxygen with at least one of aniso-shunt equation and an iso-shunt plot.